Comparative analysis of reproduction number estimation and parameter inference in SEIR-based disease modeling

Accurate estimation of the reproduction number and the influence of epidemiological parameters are critical for understanding disease dynamics. Although various statistical methods exist for parameter estimation, identifying the most suitable approach remains a challenge. To address this, we examine two complementary strategies: estimating reproduction numbers and inferring key parameters through an extended susceptible–exposed–infectious–recovered model. Five statistical techniques are applied including exponential growth, maximum likelihood, sequential Bayesian, time dependent and Gamma-distributed generation time methods to estimate basic and effective reproduction numbers. Validation with real epidemic data reveals that the time-dependent method is the most accurate, based on the mean square error and the root mean square error. Sensitivity analysis underscores the significant role of the generation time distribution. In the second strategy, Bayesian inference via Markov Chain Monte Carlo using the No-U-Turn Sampler is employed to quantify parameter uncertainty. Diagnostic tools confirm strong convergence, while posterior predictive checks validate the model’s robustness and enhanced predictive accuracy with increased training data.